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Answer:
First 4-digit multiple of 5 is 1000. It is the least 4-digit number and it is multiple of 5.
Last 4-digit number is 9999 which is not a multiple of 5 and so are 9998, 9997, 9996. Largest 4-digit number which is multiple of 5 is 9995.
Number of 4-digit multiples of 5 = 9995 − 1000 /5 + 1 = 8995/ 5 + 1 = 1799 + 1 = 1800
Step-by-step explanation:
A number x is said to be a multiple of number n if n divides the number x
. One important observation is if x is a multiple of n then the next multiple of n is x + n
. Hence the multiples of number n occur in differences of n
Suppose x and y are multiples of n
. Number of multiples of n between x and y
including them is given by y − x / n + 1
Because for every n numbers in between x and y there is a multiple of n
Combination helps to know the number of ways objects can be arranged. The 4-digit numbers that are multiples of 5 are 1800.
What is a combination?
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nC_r = \dfrac{n!}{r!(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
In order to make a 4 digit number divisible by five the number must end with either 5 or 0, and for the number to be a 4 digit number, it can not start with 0. therefore, the first place can be occupied by any number from 1 to 9, the second place can be occupied by any number from 0 to 9, the third number can be occupied by any number from 0 to 9, and the fourth number can be occupied by any number from 0 or 5. Thus, the possible options are,
[tex]= ^9C_1 \times ^{10}C_1 \times ^{10}C_1 \times ^2C_1\\\\= 9 \times 10 \times 10 \times 2\\\\= 1800[/tex]
Hence, the 4-digit numbers that are multiples of 5 are 1800.
Learn more about Combination:
https://brainly.com/question/11732255
